Nagan-4
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If "City of Sin" is "Sin City," then where is the parody of the action genre?
Standard action movie plotlines are taken and masterfully brought to the point of absurdity. If it's a street war, it's not between gangs, but between a criminal syndicate and prostitutes, and the prostitutes stage a massacre of the mafia. If it's a severed head, it's so talkative that they have to tape its mouth shut.
"Deadly little Miho," "Do I take this cop down and risk it all?" - these rather vulgar phrases from generic action movies have become classics in "Sin City."
If you want to be strict, then yes, it's a separate genre - noir.
By the way, "Pulp Fiction" is also anything but a parody.
I perceived the story about Bruce Willis's gold watch as a parody of classic stories about duty and honor in action movies. Just look at Steven Seagal, any of his films, there are plenty of these plotlines. A killer who forgot his weapon. An ordinary click of a toaster leads to the murder of Travolta. Criminal dialogues, essentially meaningless, but within the framework of the film, they are deep and wise.
If it were filmed a little less talentedly, it would be nonsense, but as it is, it's definitely a masterpiece.
It's all just my opinion.